Circular Shear Calculator
Neutral-axis shear stress of one solid circle. The area moment comes from the circular-section engine. Runs locally.
Trust summary Engine tested · Source checked · 4/4 tests · Production surface contract 6/6 · v1.0.0
- Input interpretation
- Enter values to calculate.
- Result
- —
- Model
- Neutral-axis shear stress of one solid circle.
- Scope
- Calculation runs locally in the browser; values are not uploaded.
- Verification
- Engine tested · 4/4 tests · Production surface contract 6/6 · Source checked · v1.0.0
- Named expert review
- Optional · Not performed
- Sources
- Hibbeler, Mechanics of Materials
- Evidence
- 2 golden · 2 boundary · Production surface contract 6/6 · Artifact integrity PASS
- Production
- Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain CURRENT) @ 2026-09-23T21:48:15.717Z
- Semantic contract
- PASS
Formulas
Core equations used by this calculator.
How to use
Enter the shear force and the radius
r must be positive. V may be negative. The line is a centroidal diameter.
Read the stress
τ = VQ/(I b). For this circle that is 4V/(3A). The sign of V is the sign of τ.
Example calculations
Common configurations with formula and result.
Radius 2
V = 12, r = 2
Reversed shear
V = −12, r = 2
Circular Shear calculator specification
Version 1.0.0 · Engine tested
- Engine tested 4/4 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- At the neutral axis of one solid circle, Q = (2/3) r³ and the width is 2r. τ = VQ/(I b). I comes from the circular-section engine. The result is also 4V/(3A).
- What it calculates
- Neutral-axis shear stress of one solid circle.
- Inputs
- V
- r
- Outputs
- tau
- Q
- I
- b
- area
- Formula
Q = (2/3) r³. b = 2r. I from the circular-section engine. τ = VQ/(I b).- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- The width at the axis is 2r. I comes from the circular-section engine. τ is evaluated by the transverse-shear engine. A hollow circle is its own page.
- Units
- V and r set the stress unit. τ has the unit of V/area.
- Boundary conditions
- missing V or r → MISSING_REQUIRED_INPUT
- r ≤ 0 → VALUE_MUST_BE_POSITIVE
- Example
- V=12 r=2 → τ=4/π
- Validation cases
3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence
- V=12 r=2 → τ=4/π
- V=-12 r=2 → τ=-4/π
- r=0 → VALUE_MUST_BE_POSITIVE
- Sources
- Hibbeler, Mechanics of Materials — Shear stress in a circular beamSupports: The largest shear stress in a solid circle is at the neutral axis and equals four thirds of the average shear stress.
- Hibbeler, Mechanics of Materials — Shear stress in a circular beam
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the neutral-axis shear stress of one solid circle.
Supported and not supported
Supported: Q = (2/3) r³ and b = 2r, with I from the circular-section engine and τ from the transverse-shear engine. The sign of V is the sign of τ.
Not supported: a hollow circle and a line that is not a centroidal diameter. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.circular_shear · tool id: circular-shear · pin 1.0.0.
{ "V": 12, "r": 2 }
Share the link with V and r. The result is not written into the link.
Related tools
Other calculators in this family: Transverse shear, Circular section, Rectangular shear .
Frequently asked questions
Key distinctions behind the calculation.
Where is the stress evaluated?
At a centroidal diameter. That is the largest shear stress in a solid circle.
Do I enter the area moment?
No. I is the centroidal moment of this solid circle, π r⁴/4. This page forms Q = (2/3) r³ and b = 2r, then τ = VQ/(I b).
Is a hollow circle included?
No. A hollow circle is its own page.